Preheat the oven to 350°F.
Grease a 2-quart rectangle glass dish (8 x 11 1/2 x 2 inches) with 1 teaspoon of the butter.
In a large sauté pan, over medium heat, melt the remaining 3 tablespoons of the butter. Add the onions and celery. Season with salt and pepper. Sauté until the vegetables are softened, about 4 minutes. Add the pecans and continue to sauté for 1 minute. Add the apples. Season with salt and pepper. Continue to sauté for 2 minutes. Remove from the heat and cool completely.
In a large mixing bowl, whisk the egg yolks and cream together. Add the cornmeal and whisk until smooth. Stir the apple mixture and cheese into the cornmeal mixture. Mix until incorporated.
In another large mixing bowl, whip the egg whites with an electric mixer until very stiff and peaks form, then fold into the apple batter. Pour the batter into the prepared pan and bake until it sets, about 45 minutes. Remove from the oven and let stand for 5 minutes. Spoon onto serving plates and garnish with parsley.
Makes 8 to 10 servings